A Multidimensional Critical Regulation Approach to Water Resources Optimization

Abstract Conventional water allocation models focus on reducing water shortage, maximizing economic benefits, and controlling environmental impacts, but rarely incorporate the coordinated evolution of multidimensional water systems. To address this gap, an integrated prediction‐simulation‐optimization framework was developed for 62 prefecture‐level cities in the Yellow River Basin, embedding multidimensional water‐system order directly into the optimization objective. Sectoral water use was estimated using the quota method, water availability was predicted with machine learning, and land‐use change was simulated using the PLUS model. Based on synergistic theory and information entropy, order degree was quantified across water resources, water environment, and water ecology subsystems, and the improved model was solved using NSGA‐II with entropy‐weighted TOPSIS. Water‐demand uncertainty was represented using sector‐specific truncated normal distributions and evaluated through Monte Carlo simulation with robust solution screening. Support vector machine achieved the best prediction performance, with 98% of cities meeting the accuracy threshold. Land‐use simulation yielded an average Kappa coefficient of 0.82; the most intense transitions during 2023–2030 occurred among grassland, cropland, and forestland. By 2030, both models project persistent water shortages in several cities. The improved model introduces total entropy‐increase violation as a fourth objective, thereby penalizing city‐level deterioration in water‐system order while maintaining balanced performance under conventional objectives. Robust solutions further reduce expected and worst‐case shortages under uncertainty, although basin‐scale deficits remain. This study moves water‐system order from post‐evaluation to an explicit optimization objective, providing decision support for coordinated water allocation under deterministic and uncertain conditions.